AlF3 ($D0_{14}$) Structure: AB3_hR8_155_c_de

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Prototype : AlF3
AFLOW prototype label : AB3_hR8_155_c_de
Strukturbericht designation : $D0_{14}$
Pearson symbol : hR8
Space group number : 155
Space group symbol : $\mbox{R32}$
AFLOW prototype command : aflow --proto=AB3_hR8_155_c_de [--hex]
--params=
$a$,$c/a$,$x_{1}$,$y_{2}$,$y_{3}$


Other compounds with this structure

  • FeF3

  • Hexagonal settings of this structure can be obtained with the option ––hex.

Rhombohedral primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac{1}{\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & - \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}} + \frac13 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &x_{1} \, \mathbf{a}_{1}+ x_{1} \, \mathbf{a}_{2}+ x_{1} \, \mathbf{a}_{3}& = &x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Al} \\ \mathbf{B}_{2} & = &- x_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}& = &- x_{1} \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Al} \\ \mathbf{B}_{3} & = &y_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}& = &\frac12 \, y_{2} \, a \, \mathbf{\hat{x}}+ \frac{\sqrt{3}}2 \, y_{2} \, a \, \mathbf{\hat{y}}& \left(3d\right) & \mbox{F I} \\ \mathbf{B}_{4} & = &- y_{2} \, \mathbf{a}_{1}+ y_{2} \, \mathbf{a}_{3}& = &- y_{2} \, a \, \mathbf{\hat{x}}& \left(3d\right) & \mbox{F I} \\ \mathbf{B}_{5} & = &y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}& = &\frac12 \, y_{2} \, a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}2 \, y_{2} \, a \, \mathbf{\hat{y}}& \left(3d\right) & \mbox{F I} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}+ y_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}& = &\frac14 \, \left(2 \, y_{3} + 1\right) \, a \, \mathbf{\hat{x}}+ \frac1{4 \sqrt{3}} \, \left(6 \, y_{3} - 1\right) \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(3e\right) & \mbox{F II} \\ \mathbf{B}_{7} & = &- y_{3} \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ y_{3} \, \mathbf{a}_{3}& = &- y_{3} \, a \, \mathbf{\hat{x}}+ \frac1{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(3e\right) & \mbox{F II} \\ \mathbf{B}_{8} & = &y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, \left(2 \, y_{3} - 1\right) \, a \, \mathbf{\hat{x}}- \frac1{4\sqrt{3}} \, \left(6 \, y_{3} + 1\right) \, a \, \mathbf{\hat{y}}+ \frac16 \, c \, \mathbf{\hat{z}}& \left(3e\right) & \mbox{F II} \\ \end{array} \]

References

  • J. A. A. Ketelaar, Die Kristallstruktur der Aluminiumhalogenide: I. Die Kristallstruktur von AlF3, Zeitschrift für Kristallographie – Crystalline Materials 85, 119–131 (1933), doi:10.1524/zkri.1933.85.1.119.

Found in

  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=AB3_hR8_155_c_de --params=

Species:

Running:

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